Applications of Semiclassical Asymptotics in Stochastic Modelling

半经典渐近学在随机建模中的应用

• 批准号: 9500792
• 负责人: Robert Maier
• 金额: $ 6万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500792&HistoricalAwards=false
• 关键词: Applications; Semiclassical; Asymptotics; Stochastic; Modelling

DMS-9500792 Maier The proposed research will apply the tools of singular perturbation theory to the estimation, in various asymptotic limits, of the probability of unlikely events associated with drift-diffusion and other stochastic models. It is often the case that the leading asymptotics of such probabilities are rigorously specified by large deviations theory. Singular perturbation theory, in particular Maslov-WKB theory, permits the formal computation of subdominant asymptotics. Specific stochastic models to be studied include models arising in teletraffic engineering and chemical physics. Physical, chemical, or engineering systems often have a random element. As a consequence, it may be difficult to predict their long-time behavior, or the rate at which unlikely events (large departures from equilibrium, severe equipment malfunction, etc.) are likely to occur. It is important to be able to estimate the frequency of such events. The proposed research will develop and apply mathematical tools to this end.

DMS-9500792 Maier建议的研究将应用奇异摄动理论的工具，在不同的渐近极限下估计与漂移-扩散和其他随机模型有关的不太可能事件的概率。通常的情况是，这种概率的主要渐近性由大偏差理论严格规定。奇异摄动理论，特别是Maslov-WKB理论，允许形式计算次优渐近性。要研究的具体随机模型包括电信交通工程和化学物理中出现的模型。物理、化学或工程系统通常都有一个随机元素。因此，可能很难预测他们的长期行为，或不太可能发生的事件(严重偏离平衡、严重设备故障等)的比率。都有可能发生。能够估计这类事件的频率是很重要的。拟议的研究将为此目的开发和应用数学工具。